Lattice ‘Roman’ Multiplication
I learnt the below when I was 10 or 11 years old and still use it today. It’s possibly the easiest way ever of multiplying large numbers and is dead easy to learn.
My teacher always said the Romans used it, but from reading more about it I’m not so sure!
The below is a direct copy from http://mathforum.org/library/drmath/view/52468.html and it explains it perfectly.
The Lattice Form of Multiplication dates back to the 1200s or before in Europe. It gets its name from the fact that to do the multiplication you fill in a grid which resembles a lattice.
Let me see if I can explain it with an example. Let’s multiply 469 x 37.
First write the 469 across the top, and the 37 down the right side of a 3×2 rectangle. (It’s 3×2 because the factors have three and two digits respectively.)
Now fill in the lattice by multiplying the two digits found at the head of the column and to the right of the row. When the partial product is two digits, the first (10’s) digit goes above the diagonal and the second (1’s) digit goes on the lower right of the diagonal. If the partial product is only one digit, a zero is placed in the triangle above the diagonal in the square.
At this point, we have the multiplication done. Now we add along the diagonals beginning in the lower right to get the final product. Any “carries” when adding are illustrated outside the rectangle.
Multiplication really takes three steps: multiply, carry, add. The method we typically use does the multiply and carry steps together. The lattice method does all three steps separately, so it’s really easier!
See http://mathforum.org/dr.math/ for other stuff for kids.
Another good example of this method is at http://www.calculatorsoup.com/calculators/math/latticemultiplication.php